This paper breaks the correlation risk premium down into two components: a premium related to the correlation of continuous stock price movements and a premium for bearing the risk of co-jumps. We propose a novel way to identify both premiums based on dispersion trading strategies that go long an index option portfolio and short a basket of option portfolios on the constituents. The option portfolios are constructed to only load on either volatility or jump risk. We document that both risk premiums are economically and statistically significant for the S&P 100 index. In particular, selling insurance against co-jumps generates a sizable annualized Sharpe ratio of 0.85.